Topological Adventures in Neuroscience

Hess, Kathryn

doi:10.1007/978-3-030-43408-3_11

Cited by 8 publications

(6 citation statements)

References 13 publications

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“…2a, see "Methods" section [20][21][22][23] ). This persistent homology approach has been previously used to identify differences in cognition across individuals based on resting state functional connectivity 24 , to find percolation properties of porous materials 25 , to differentiate neuron morphologies 26 , and to understand many other real-world systems [27][28][29] . We note that in our setup, only the rank order of edges induced by the original edge weights are preserved, so that the specific edge weights or their generating distribution does not affect the outcome.…”

Section: Resultsmentioning

confidence: 99%

Variability in higher order structure of noise added to weighted networks

2021

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The complex behavior of many real-world systems depends on a network of both strong and weak edges. Distinguishing between true weak edges and low-weight edges caused by noise is a common problem in data analysis, and solutions tend to either remove noise or study noise in the absence of data. In this work, we instead study how noise and data coexist, by examining the structure of noisy, weak edges that have been synthetically added to model networks. We find that the structure of low-weight, noisy edges varies according to the topology of the model network to which it is added, that at least three qualitative classes of noise structure emerge, and that these noisy edges can be used to classify the model networks. Our results demonstrate that noise does not present as a monolithic nuisance, but rather as a nuanced, topology-dependent, and even useful entity in characterizing higher-order network interactions.

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Section: Resultsmentioning

confidence: 99%

Variability in higher order structure of noise added to weighted networks

2021

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“…Computational topology and higher-order networks have proven successful for analyzing the full spectrum of brain data ranging from functional networks [243], to morphology of branching neurons [148], to structural (synaptic connectivity) [223], to place cells [112], to the C. elegans connectome [130], to imaging of brain disease [44,75]. Rather than an exhaustive list of research in topological neuroscience, we refer to the reader to a few recent survey articles [36,76,132].…”

Section: Applications Of Persistent Homologymentioning

confidence: 99%

What are higher-order networks?

Bick¹,

Gross²,

Harrington³

2021

Preprint

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Modeling complex systems and data using the language of graphs and networks has become an essential topic across a range of different disciplines. Arguably, this network-based perspective derives is success from the relative simplicity of graphs: A graph consists of nothing more than a set of vertices and a set of edges, describing relationships between pairs of such vertices. This simple combinatorial structure makes graphs interpretable and flexible modeling tools. The simplicity of graphs as system models, however, has been scrutinized in the literature recently. Specifically, it has been argued from a variety of different angles that there is a need for higher-order networks, which go beyond the paradigm of modeling pairwise relationships, as encapsulated by graphs. In this survey article we take stock of these recent developments. Our goals are to clarify (i) what higher-order networks are, (ii) why these are interesting objects of study, and (iii) how they can be used in applications.

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“…2a, Methods, and [51,23,45,29]). This persistent homology approach has been previously used to identify differences in cognition across individuals based on resting state functional connectivity [4], to find percolation properties of porous materials [48], to differentiate neuron morphologies [33], and to understand many other real-world systems [13,28,44]. We note that in our setup, only the rank order of edges induced by the original edge weights are preserved, so that the specific edge weights or their generating distribution does not affect the outcome.…”

Section: Mathematical Frameworkmentioning

confidence: 99%

Variability in higher order structure of noise added to weighted networks

Blevins¹,

Kim²,

Bassett³

2021

Preprint

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From spiking activity in neuronal networks to force chains in granular materials, the behavior of many real-world systems depends on a network of both strong and weak interactions. These interactions give rise to complex and higher-order system behaviors, and are encoded using data as the network's edges. However, distinguishing between true weak edges and low-weight edges caused by noise remains a challenge. We address this problem by examining the higher-order structure of noisy, weak edges added to model networks. We find that the structure of low-weight, noisy edges varies according to the topology of the model network to which it is added. By investigating this variation more closely, we see that at least three qualitative classes of noise structure emerge. Furthermore, we observe that the structure of noisy edges contains enough model-specific information to classify the model networks with moderate accuracy. Finally, we offer network generation rules that can drive different types of structure in added noisy edges. Our results demonstrate that noise does not present as a monolithic nuisance, but rather as a nuanced, topologydependent, and even useful entity in characterizing higher-order network interactions. Hence, we provide an alternate approach to noise management by embracing its role in such interactions.

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Topological Adventures in Neuroscience

Cited by 8 publications

References 13 publications

Variability in higher order structure of noise added to weighted networks

Variability in higher order structure of noise added to weighted networks

What are higher-order networks?

Variability in higher order structure of noise added to weighted networks

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